Assume that the company uses only two inputs to producey, input1which has a market price1= $30and input2with market price2= $10.

2. (4pts) What is an Isocost? (Provide a definition).
4. (3pts) What is the Isocost for the information given in the question announcement?
6. (3pts) What is the slope of the Isocost? What you can say about this?
8. (3pts) Graph the result of part b for Total Cost of 300?
10. (4pts) What happens if only the price of1doubles (total cost does not change)? Explain.Show graphically using numbers from (d).
12. (4pts) What happens if both prices of1and 2doubles (total cost does not change)? Explain. Show graphically using numbers from (d).
14. (4pts) What happens if both prices of1and 2do not changeand total cost doubles? Explain. Show graphically.

2. (10 pts) Explain with words and using graphs (based on the conditional input demand discussed in class). Fell free to use calculus too.

2. (4 pts) What happens to the demand curve of1if its own-price increases?
4. (3 pts) What happens to the demand curve of1if the price of2increases?
6. (3 pts) What happens to the demand curve of1if the outputyincreases?

3. (20pts) A farmer minimizes the cost subject to their productiony=100x11/3x21/3. The company uses only two inputs to producey, input1has a market price1= $100and input2has a market price2= $500.

2. (15pts) Find Total Cost as a function ofy only.
4. (2pts) Find the Marginal Cost (MC) and graph it withyin the horizontal axis andMCin the vertical axis.
6. (3pts) What is the cost elasticity? What is the interpretation (provide an example)? What about economies of scale?

4. (15 pts) Assume that the company production function is given byy=100x11/3x21/3. The market price (p) for outputis $30. The company uses only two inputs to producey, input1has a market price1= $100and input2has a market price2= $500.

2. (1pts) Set up the profit equation.
4. (7pts) Find the input level of1and 2that maximizes profit
6. (2pts) How much is the company producing when maximizing profit?
8. (1pts) What is the company's profit?
10. (4pts) What happens to the quantity demanded of1if its price increase by 50%? What happens to the production and profit?

5. (30pts) In the previous question, the farmer was maximizing profit without any constraint on cost of production.

2. (15pts) Using the Lagrange multiplier find the conditional input demand for1 and2in function of the quantity produced. (Hint:minimize cost subject toy=100x11/3x21/3, results should be similar to those found in 6)
4. (5pts) Find the total cost in function of the quantity produced.
6. (3pts) What is the total cost for the quantity produced in the previous question?
8. (3pts) What is the quantity produced if the total cost is now half of the amount found in (c)?
10. (4pts) What happens to input conditional demands compared to the previous question? Represent results of the previous question and found here in a graph with Isocosts and Isoquants.

(ONLY REFERENCE I COULD FIND: https://www.youtube.com/watch?v=YPM73mpqm4A)

(TRY TO COMPLETE ALL PARTS IF POSSIBLE. THANK YOU!! :))